The Apple TV outputs at 20-bit, while the Mac mini will output at the resolution of the connected soundcard. The in-built one delivers 24-bit.
You can buy lossless (CD-resolution) or higher over the internet, from a growing number of suppliers.
I have both the mini and the ATV - like the latter for going to the thousands of free video and audio podcasts on the net, as well as YouTube, and buying content from Apple. Brilliant. Saw Appalloosa in HD this weekend, excellent quality and instantly downloaded.
Am also using Boxee, for comparison purposes.There are many such media-aggregator solutions out there now, and they all show to the sheer impossibility of B&O managing to keep up with what such fast-moving small companies deliver via software. Boxee is very buggy so far, but they are honest about it, as the version available is a beta.
If I had to choose between ATV and mini, I would go for the latter. It is a computer, it lets you surf the web, it will handle any resolution, it will handle all your content libraries, and with front-ends such as Boxee, you can make it aggregate from the net, depending upon what you have available where you live. My mini does excellent music playback, and I also use it to rip cd's/music dvd's to my server. Very happy with it - bought one of the Logitech diNovo bluetooth keyboards to operate it.
ATV doesn't let you browse, and while there is some freedom to what you can access through podcasts, etc, it is a shop front-end for iTunes, but it's great. The combination of ATV and mini has my broadcast/cable viewing down to about 5% of my total.
Here's an article about Boxee: http://www.nytimes.com/2009/01/17/technology/internet/17video.html